Abstract: In this paper we introduce automata networks to model some features of the emergence of a vocabulary related with the naming game model. We study the dynamical behaviour (attractors and convergence) of extremal and majority local functions.

Abstract: Traditionally, the formation of vocabularies has been studied by agent-based models (primarily, the naming game) in which random pairs of agents negotiate word-meaning associations at each discrete time step. This article proposes a first approximation to a novel question: To what extent is the negotiation of word-meaning associations influenced by the order in which agents interact? Automata networks provide the adequate mathematical framework to explore this question. Computer simulations suggest that on two-dimensional lattices the typical features of the formation of word-meaning associations are recovered under random schemes that update small fractions of the population at the same time; by contrast, if larger subsets of the population are updated, a periodic behavior may appear.

Abstract: This work attempts to give new theoretical insights into the absence of intermediate stages in the evolution of language. In particular, a mathematical model, based on automata networks, is proposed with the purpose to answer a crucial question: How a population of language users can reach agreement on linguistic conventions? To describe the appearance of drastic transitions in the development of language, an extremely simple model of working memory is adopted: at each time step, language users simply lose part of their word memories according to a forgetfulness parameter. Through computer simulations on low-dimensional lattices, sharp transitions at critical values of the parameter are described.